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bulgar [2K]
3 years ago
10

Jill says that 12.6666666 is less than 12.63 explain Her error

Mathematics
1 answer:
Ymorist [56]3 years ago
7 0
Look at the last number in the decimal.

12.66
12.63

Compare 6 and 3. 6 is larger so therefore 12.6666666 is larger. (You also need to compare the tenths place too, but these happen to have the same tenths place, .6.
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Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term 2x^2, which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form  f(x)=ax^2+bx+c is given by the expression:

x_v=\frac{-b}{2a}

Since in our case a=2 and b=-3, we get that the x-position of the vertex is:

x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6

See the graph produced in the attached image.

4 0
3 years ago
Write the expression 53.7124 x 10^{3} as a single number
mars1129 [50]

Answer:

53712.4

Explanation:

\sf\rightarrow  53.7124\:x\:10^3

  • 10³ = 1000

\sf\rightarrow  53.7124\:x\:1000

\sf\rightarrow  53712.4

6 0
2 years ago
Read 2 more answers
PLEASE HELP ASAP
lesya692 [45]

Answer:

x^2+14x+49    ( it could be polynomial because it has 3 terms and each term has a whole number and a coefficient)

Step-by-step explanation:

(x+7)^2

(x+7)(x+7)

x^2+7x+7x+49

x^2+14x+49

I am not sure it's a polynomial or not

7 0
3 years ago
PLEASE HELP<br> what does QS equal
Ainat [17]

Answer:

22

Step-by-step explanation:

QS =2×11 = 22

__________

5 0
3 years ago
Read 2 more answers
Please can someone solve this​
Leni [432]

Answer:

45

Step-by-step explanation:

2a+3b=15, multiply everything by 3

3(2a+3b)=3(15)

6a+9b=45

7 0
3 years ago
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